Problem: $g(n) = 5n+f(n)$ $f(t) = -t^{2}+5t-1+2(h(t))$ $h(x) = 5x$ $ h(g(-2)) = {?} $
First, let's solve for the value of the inner function, $g(-2)$ . Then we'll know what to plug into the outer function. $g(-2) = (5)(-2)+f(-2)$ To solve for the value of $g$ , we need to solve for the value of $f(-2)$ $f(-2) = -(-2)^{2}+(5)(-2)-1+2(h(-2))$ To solve for the value of $f$ , we need to solve for the value of $h(-2)$ $h(-2) = (5)(-2)$ $h(-2) = -10$ That means $f(-2) = -(-2)^{2}+(5)(-2)-1+(2)(-10)$ $f(-2) = -35$ That means $g(-2) = (5)(-2)-35$ $g(-2) = -45$ Now we know that $g(-2) = -45$ . Let's solve for $h(g(-2))$ , which is $h(-45)$ $h(-45) = (5)(-45)$ $h(-45) = -225$